# Spectral properties and scattering theory for wave propagation in inhomogeneous media

- Authors
- Publication Date
- Jan 01, 1992
- Source
- OpenGrey Repository
- Keywords
- Language
- English
- License
- Unknown

## Abstract

The wave equation (#partial deriv#_t"2 + H) u = 0 with H: = f"2(x) "n#SIGMA#_j_,_k_=_1 D_jg_j_k(x)D_k, x element of R"n describes the propagation of acoustical waves as well as electromagnetic waves in inhomogeneous media. The L"#infinity# functions f and g_j_k are short range (Enss type) perturbations of other functions f_0 and g_j_k"0, respectively. The functions f_0 and g_j_k"0 are more regular but generally non-constant, having a long range type approach to some limits in radial directions at infinity. Mourre type estimates are used to show that the spectrum of H is equal to [0, #infinity#) and is absolutely continuous, except possibly for a discrete set of eigenvalues of finite multiplicity that can accumulate only at zero or at infinity. Away from these eigenvalues an optimal limiting absorption principle for H is established. Moreover, the existence and the completeness of the wave operators between H and H_0 are proven, where H_0: = f_0"2(x) "n#SIGMA#_j_,_k_=_1 D_jg_j_k"0(x)D_k. (orig.) / Available from TIB Hannover: RO 5073(551) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische Informationsbibliothek / SIGLE / DE / Germany